On constitutive modelling of porous neo-Hookean composites

In this paper a hyperelastic constitutive model is developed for neo-Hookean composites with aligned continuous cylindrical pores in the finite elasticity regime. Although the matrix is incompressible, the composite itself is compressible because of the existence of voids. For this compressible transversely isotropic material, the deformation gradient can be decomposed multiplicatively into three parts: an isochoric uniaxial deformation along the preferred direction of the material (which is identical to the direction of the cylindrical pores here); an equi-biaxial deformation on the transverse plane (the plane perpendicular to the preferred direction); and subsequent shear deformation (which includes “along-fibre” shear and transverse shear). Compared to the multiplicative decomposition used in our previous model for incompressible fibre reinforced composites [Guo, Z., Peng, X.Q., Moran, B., 2006, A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. J. Mech. Phys. Solids 54(9), 1952–1971], the equi-biaxial deformation is introduced to achieve the desired volume change. To estimate the strain energy function for this composite, a cylindrical composite element model is developed. Analytically exact strain distributions in the composite element model are derived for the isochoric uniaxial deformation along the preferred direction, the equi-biaxial deformation on the transverse plane, as well as the “along-fibre” shear deformation. The effective shear modulus from conventional composites theory based on the infinitesimal strain linear elasticity is extended to the present finite deformation regime to estimate the strain energy related to the transverse shear deformation, which leads to an explicit formula for the strain energy function of the composite under a general finite deformation state.     

An inverse dispersed multiphase flow model for liquid production rate determination

The aim of this study is to develop a model for the determination of the superficial velocities in horizontal and slightly inclined oil–water pipe flow conditions by using pressure gradient and mixture density information. In this article an inverse model is suggested for a dispersion of oil in water and of water in oil. This approach permits to select dispersed flow conditions from a set of experimental data, and uses a new hybrid model for the effective viscosity. A set of 310 oil–water experimental data points collected on an experimental set-up of length L = 15 m and diameter D = 8.28 cm at various (slight) orientations is used to validate the inverse method. The comparison between model reconstructions and measured flow velocities show a reasonable agreement.     

Diffusion in isotropic and anisotropic porous systems: Three-dimensional calculations

Effective diffusion coefficients were calculated numerically for three-dimensional unit cells representative of different unconsolidated porous media. These numerical results were compared with the experimental results of Kim for packed beds of glass spheres, mica particles, and an artificial porous medium composed of mylar disks. These three-dimensional numerical results confirm that the porosity is the essential parameter for the determination of the effective diffusion coefficient in the case of unconsolidated isotropic systems. In the case of anisotropic systems, better agreement is obtained between numerical predictions and actual data when the unit cell is three-dimensional rather than twodimensional. This emphasizes the fact that three-dimensional unit cells feature more realistic geometrical properties which are needed to accurately describe anisotropic systems.     

Two-dimension estimate of effective properties of solid with random voids

A discrete model for the estimation of the effect of random voids on the structural properties of a two-dimensional solid is presented. Triangular void cells are used to simulate randomly located micro-cracks.The proposed model is solved using Cell Method, a recent numerical method that allows a direct discrete formulation of balance equations. Both heterogeneities of the structure and stress concentrations due to voids distribution are taken into account by the model. Following an introduction, some aspects of Cell Method for plane elasticity that are relevant for this paper will be briefly recalled and results from simulations in the elastic field will be discussed. Next, the proposed model will be extended to plastic field and more simulations will be presented. Results show that this model can be successfully employed to assess the structural response of a 2D solid with randomly distributed voids.     

Measurement of the effective thermal conductivity of a Mg–MgH2 packed bed with oscillating heating

The magnesium–magnesium hydride–hydrogen-system (Mg–MgH₂–H₂) offers, because of its combined hydrogen and heat storage capacity, the possibility to design hydride heat pumps and heat stores. For such industrial application systems based on cylindrically formed reactors filled with an active magnesium powder, the effective thermal conductivity limits the time in which the metal hydride alloy is charged and discharged with hydrogen. Determination of this transport coefficient is of fundamental importance for the optimum design of magnesium hydride reactors. The complex interrelation of the different transport mechanisms in a metal hydride packed bed and the hitherto undefined rule that the solid effective thermal conductivity behaves as a function of the hydrogen concentration, requires a reliable and simple-to-realize measuring method so as to determine the effective thermal conductivity of a magnesium hydride bed. In the present study, a report is given for the first time on the initiation of a measuring technique with oscillating change of temperature in a non-permeated packed bed of fine-grained material. The measurement of the effective thermal conductivity can ensue by tailoring the problem-specific mathematical result to the experimentally recorded temperature-time function. The effective thermal conductivity of the magnesium hydride bed varies between 2 and 8 W/(m K) in a temperature range of 523–653 K.     

Interfacial debonding of two-phase composite with periodic structure

A mixed analytical-numerical (boundary element method) procedure is presented for estimating the effective elastic moduli of a two-phase periodic composite by application of a unit cell. The two-phase composite consists of a metal/polymer matrix and one/three circular ceramic inclusions with adhesive and partial debonding of the interface. The results are displayed numerically with special attention given to development of plastic zones as debonding occurs. Dependence of load-time history is exhibited.     

On convergent numerical algorithms for unsymmetric collocation

In this paper, we are interested in some convergent formulations for the unsymmetric collocation method or the so-called Kansa’s method. We review some newly developed theories on solvability and convergence. The rates of convergence of these variations of Kansa’s method are examined and verified in arbitrary–precision computations. Numerical examples confirm with the theories that the modified Kansa’s method converges faster than the interpolant to the solution; that is, exponential convergence for the multiquadric and Gaussian radial basis functions (RBFs). Some numerical algorithms are proposed for efficiency and accuracy in practical applications of Kansa’s method. In double–precision, even for very large RBF shape parameters, we show that the modified Kansa’s method, through a subspace selection using a greedy algorithm, can produce acceptable approximate solutions. A benchmark algorithm is used to verify the optimality of the selection process.     

New Brownian bridge construction in quasi-Monte Carlo methods for computational finance

Quasi-Monte Carlo (QMC) methods have been playing an important role for high-dimensional problems in computational finance. Several techniques, such as the Brownian bridge (BB) and the principal component analysis, are often used in QMC as possible ways to improve the performance of QMC. This paper proposes a new BB construction, which enjoys some interesting properties that appear useful in QMC methods. The basic idea is to choose the new step of a Brownian path in a certain criterion such that it maximizes the variance explained by the new variable while holding all previously chosen steps fixed. It turns out that using this new construction, the first few variables are more “important” (in the sense of explained variance) than those in the ordinary BB construction, while the cost of the generation is still linear in dimension. We present empirical studies of the proposed algorithm for pricing high-dimensional Asian options and American options, and demonstrate the usefulness of the new BB.     

Validity of the One and One-Half Layer Quasi-Geostrophic Model and Effective Topography

ABSTRACT

We rigorously justify the so-called one and one-half layer quasi-geostrophic model from the two layer model as the ratio of the depth of the bottom layer over that of the top layer approaches infinity. The effective dynamics is given by the classical barotropic quasi-geostrophic dynamics for the bottom layer without topography, and the one layer quasi-geostrophic dynamics with the stream function of the bottom layer serving as an effective (possibly time-dependent) topography for the the top layer. Such a one and one-half layer model is utilized in successful quantitative prediction of the Great Red Spot on Jupiter (see Turkington et al., 2001 Turkington , B. , Majda , A. J. , Haven , K. , DiBattista , M. ( 2001 ). Statistical equilibrium predictions of jets and spots on jupiter. Proc. Natl. Acad. Sci. USA 98 ( 22 ): 12346 – 12350 . [PUBMED] [INFOTRIEVE] [CSA] [CROSSREF] [Crossref] , [Google Scholar]).